Behind the energy production and product processing processes that have formed the backbone of industry since the industrial revolution lie the fascinating rules of thermodynamics. From a combustion chamber in a power plant to the large industrial ovens where agricultural products are dried, these rules determine the efficiency and safety of processes. In all these designs, the Lewis number (Le), known as the ratio of thermal diffusivity to mass diffusivity, emerges as a hidden decision-maker.
In this article, we will examine why the Lewis number plays a vital role in industrial combustion and drying processes. To check your values for your facility designs or assignments, you can benefit from our Lewis Sayisi Hesaplama tool.
Lewis Number in Combustion Dynamics and Flame Stability
Combustion is essentially a complex chemical reaction where fuel (mass) combines with oxygen to rapidly release energy (heat). For a flame to propagate in a mixture, both heat must be conducted toward the unburned gases, and fuel and oxygen molecules must diffuse to the flame front. The Lewis number represents exactly the race between these two events.
Combustion at Le = 1 (Stable Flame)
If the Lewis number for a fuel-air mixture is 1 ($Le = 1$), the rate at which the heat produced by the reaction is conducted ahead of the flame and the rate at which fresh fuel molecules reach the flame front are in perfect balance. In this case, a flat and stable (laminar) flame front forms, and the flame speed occurs quite close to theoretical calculations. Methane-air mixtures typically have a Lewis number very close to 1.
Combustion at Le < 1 (Cellular Flame Structures)
In cases where fuels with extremely light molecules, such as hydrogen, burn, mass diffusion occurs much faster, and the Lewis number drops below 1. In this scenario, thermo-diffusive instabilities arise.
- With a slight perturbation on the flame surface, reactants penetrate the region faster than the heat loss.
- This increases the local burning rate, causing the flame to acquire a "cellular" or wavy structure.
- Although combustion efficiency may increase, flame control becomes difficult. Engineers designing next-generation hydrogen turbines must closely examine Lewis number dynamics to prevent these instabilities.
Combustion at Le > 1 (Flame Extinction)
In air mixtures using heavy hydrocarbon fuels (e.g., propane, octane), heat diffuses faster than mass ($Le > 1$). Here, even if the flame heats up fast enough to burn the reactants, new fuel molecules cannot reach the region quickly enough.
- When there is a fluctuation on the flame surface, temperature drops occur in the combustion zone.
- This can lead to local extinctions caused by "stretch".
The Dance of Moisture and Heat in Industrial Drying Processes
Drying processes (e.g., drying timber, paper, grain, or ceramics) involve the process of evaporating water in a solid material and transferring it to the air. Hot air is blown onto the surface transferring heat (heat transfer), while water vapor inside and on the surface of the material mixes with the air and moves away (mass transfer).
In the drying process, optimization and energy saving directly depend on the harmony (analogy) of these two transport events.
Chilton-Colburn Analogy and Psychrometry
In situations where water evaporates into the air, the Lewis number is approximately between $0.85$ and $1.0$. Finding a value so close to 1 is a great boon given to engineers by nature.
- By assuming the Lewis number is 1 ($Le \approx 1$), the wet-bulb temperature of the air can be considered equivalent to the adiabatic saturation temperature.
- Energy balance and moisture removal calculations in the drying oven are equated. If you know the heat transfer coefficient ($h$), you can directly obtain the mass transfer coefficient ($h_m$) without performing arduous mass transfer measurements. The formula goes like this: $h / (h_m \cdot \rho \cdot c_p) = Le^{2/3} \approx 1$.
Deep Drying and Diffusion Inside the Material
If the solid material (e.g., a brick or a log) is quite thick, the issue moves away from surface evaporation and turns into capillary moisture diffusion "inside" the material. An internal Lewis (or Luikov) number can be defined comparing the thermal diffusivity (heat conduction) inside the material with moisture diffusivity.
If the material conducts heat quickly but releases moisture (mass) slowly (High Le), the outer surface overheats, dries, and cracks before the moisture in the inner parts can escape. To prevent these undesirable cracks (case hardening), engineers must slowly increase the temperature of the drying oven or temporarily raise the ambient humidity.
Conclusion
Dimensionless numbers are not abstract concepts left in laboratory notebooks; they directly affect the efficiency of a jet engine or the quality of the paper on your desk. The fine-tuning role of the Lewis number over heat and mass diffusion empowers the engineer in reaction and separation processes.
If you want to see the change in your transport coefficients in different fuel mixtures you work with or under special atmospheric conditions (e.g., combustion/drying in an Argon-Oxygen atmosphere), you can instantly observe which side your system leans toward by entering your parameters into the Lewis Sayisi Hesaplama tool.
